CN107123994B - Linear solving method of interval reactive power optimization model - Google Patents

Linear solving method of interval reactive power optimization model Download PDF

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CN107123994B
CN107123994B CN201710290432.4A CN201710290432A CN107123994B CN 107123994 B CN107123994 B CN 107123994B CN 201710290432 A CN201710290432 A CN 201710290432A CN 107123994 B CN107123994 B CN 107123994B
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张聪
陈皓勇
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South China University of Technology SCUT
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Abstract

The invention discloses a linear programming based interval power flow calculation method in a rectangular coordinate form, which comprises the following steps of: 1. and establishing an interval reactive power optimization model. And expressing the active power output and the load of the generator into an interval form, and substituting the active power output and the load into a power flow equation in a deterministic reactive power optimization model to obtain an interval reactive power optimization model. 2. The variables in the interval reactive power optimization model are divided into two types. One is a control variable that can be controlled manually, and the other is a state variable that varies with the control variable. 3. And constructing a linear model of the interval reactive power optimization model. 4. And solving the linear model of the interval reactive power optimization model by adopting a pure method, and repeatedly iterating. 5. And outputting the result. The method has the advantages of good convergence, capability of ensuring that the obtained reactive voltage control strategy completely meets the safety constraint of power grid operation, high efficiency and the like.

Description

Linear solving method of interval reactive power optimization model
Technical Field
The invention relates to a method for solving an uncertain reactive power optimization problem of a power system, which expresses uncertain parameters into intervals when solving the reactive power optimization problem containing the uncertain parameters, assumes that all variables are continuous, approaches the optimal solution of a model through a step-by-step linearization method, and obtains the optimal solution which really meets the constraint of the uncertain reactive power optimization problem.
Background
The power system itself contains many uncertainty factors such as frequently changing commercial and residential loads, wind power, photovoltaic generator output, and measurement errors of electrical parameters that are difficult to predict accurately. Due to the existence of the uncertainty factors, various optimal power flow models established based on the power grid parameters contain uncertainty, while the traditional deterministic reactive power optimization only considers a certain scene (a certain situation) in the uncertainty data, and the optimization result cannot really meet the safety and the economy of the power grid operation. For this reason, these uncertainty parameters in the grid need to be modeled in order to build an uncertainty reactive power optimization model. It is now common to represent these uncertainty parameters as random variables and assume that they obey some particular probability distribution (e.g., gaussian). After random variables are added, the constraint conditions of the model cannot need to set corresponding confidence levels, and a corresponding opportunity constraint planning model is established. When the model is solved, a decision space is generated by adopting a random simulation technology, the constraint condition is judged by utilizing Monte Carlo (Monte Carlo) simulation, and a reactive voltage control strategy meeting the constraint condition is obtained by utilizing an intelligent algorithm through cyclic iteration. However, such opportunistic constraint planning algorithms can only obtain control strategies that satisfy the safe operation constraints of the power grid at a certain confidence level. Meanwhile, with the increase of uncertainty parameters considered in the model, the number of scenes needing to be simulated by Monte Carlo simulation is greatly increased, and the consumed calculation time is sharply increased, so that the algorithm is rarely applied to an actual system. In addition to this type of algorithm, a robust optimization algorithm is also used to solve the uncertainty reactive power optimization model. The method comprises the steps of regarding uncertain parameters as parameters fluctuating within a certain upper limit and a certain lower limit, then establishing a robust optimization model enabling the boundaries (worst scenes) of all the uncertain parameters to meet system constraints, and considering that the system can meet safe operation constraints under all the uncertain parameters as long as the system meets the constraints of a reactive power optimization problem on the boundary conditions. In the solving process, a nonlinear power flow equation needs to be linearized, the constraint conditions are changed into constraint conditions under all boundaries, a deterministic robust reactive power optimization model is established, and a general nonlinear programming algorithm is adopted for solving. Because it only needs to solve a deterministic nonlinear programming model, the efficiency of the uncertain reactive power optimization problem is greatly improved. However, the optimal solution obtained by the method can only meet the constraint condition after linearization, but not the original nonlinear constraint, and the operation safety of the power grid cannot be ensured. With the continuous development of modern power systems, the continuous expansion of the scale of a power grid and the access of more and more new energy, the traditional Monte Carlo method can greatly increase the sampling number, the scale of load flow calculation is also increased, the calculation time is increased rapidly, and the method is not suitable for analyzing the influence of the output of the new energy on the voltage of the power grid. Therefore, a feasible uncertain reactive power optimization algorithm capable of meeting the constraint condition needs to be found, so that the safe and reliable operation of the power grid is realized in the true sense. The interval theory and the optimization calculation method thereof which gradually get the most attention in recent years are the best means for solving the problems.
The interval theory was originally proposed by Moore in 1966, but the calculation result obtained by the interval theory is often conservative, the application obtained in the practical situation is not optimistic, and the application in the power system is lagged. In recent years, interval theory is gradually used for interval power flow calculation, for example, a Krawkzyk-Moore operator is used for three-phase power flow calculation of a power distribution network in the method [1], and the method can calculate power flow determined by load and interval power flow containing uncertain load. In order to further improve the accuracy of interval calculation, people research the shortcomings of interval calculation, find that intervals neglect the correlation between intervals in the calculation process, and in order to solve the problem, Comba and Stolfi propose interval affine arithmetic in 1993 and use the interval affine arithmetic in the field of computer graphics. The document [2] firstly uses interval affine arithmetic for the calculation of the interval power flow of the power system, and utilizes a compressed domain method (domain-constrained) based on linear programming to improve the calculation speed, effectively reduces the solution range of the interval power flow, and makes breakthrough in the calculation time, convergence performance and precision. In terms of interval optimization, the article [3] firstly solves the interval optimization theory by using an uncertain reactive power optimization problem. The method adopts particle swarm optimization to solve, single power flow sections are analyzed, and each power flow section is obtained by solving an interval power flow equation through a Krawczyk-Moore iterative algorithm. But the convergence of the adopted iterative algorithm cannot be ensured, and meanwhile, the calculation time is too long, so that the real engineering practicability cannot be realized.
Reference documents:
wen [1] Wang Chengshan, Wang Gekken, Power distribution network three-phase load flow calculation and example analysis based on interval algorithm [ J ] China Motor engineering Proc, 2002,22(3): 58-62.
Text [2] Vaccaro A, Canizers C, Villacci D. an affine imaging for reusable Power flow analysis in the presence of the present of data acquisition availability [ J ] Power Systems, IEEE Transactions on,2010,25(2): 624-.
Wen [3] Zhang Yongjun, Sujie and Hoyi chess, a reactive power optimization method for a power grid with a distributed power supply based on interval arithmetic [ J ] protection and control of a power system, 2014,42(15) and 21-26.
Disclosure of Invention
The invention aims to overcome the defects and shortcomings of the prior art and provides a linear solving method of an interval reactive power optimization model. When the uncertain reactive power optimization model is solved, only the load in the power flow equation and the active power output of the generator are considered as uncertain parameters and are expressed into an interval form, so that the interval reactive power optimization model is established. Then, the variables in the model are classified, one is a real variable which can be controlled manually, and is called a control variable, and the classification includes three types: the voltage of the generator terminal (excluding the voltage of a balancing machine), the number of switchable capacitor (or reactance) groups and the transformation ratio of the transformer; the other type is an uncontrollable interval variable which changes along with the control variable, namely a state variable, and comprises a reactive power output of the generator, an active power output of a balanced node, a voltage of a load node and a voltage phase angle of an unbalanced node. Finally, a successive linearization method for solving the nonlinear programming problem is utilized to solve. It should be noted that, in order to adopt a linearization method, it is assumed herein that all control variables are continuous variables, and when an interval power flow equation needs to be linearized, in order to obtain a more accurate interval power flow, the interval power flow algorithm proposed in the text [2] is adopted to obtain the interval of the state variables, instead of using an interval taylor formula to expand the interval power flow equation. In a specific solving process, firstly, an interval reactive power optimization model is expanded by a Taylor formula (except an interval power flow equation), a real variable (a control variable) is expanded according to a general form, and an interval variable (a state variable) is expanded at an interval midpoint. The target function comprises the middle point and the radius of the interval of the network loss, and only the middle point of the interval of the network loss is taken as the target function. For the interval of the state variable in the linearized inequality constraint, the interval power flow algorithm [2] can be adopted for obtaining. Therefore, a linear programming iterative model is constructed, only real variables (control variables) are included, and the optimal control strategy can be obtained by solving iteration through a simplex method. Furthermore, the iteration step size of the control variable needs to be limited to ensure convergence. Because the state variables exist in the interval mode in the calculation process, as long as the whole interval meets the constraint condition, all the variables can be ensured not to exceed the limit, and the safe and reliable operation of the power grid can be realized. Meanwhile, affine arithmetic is adopted in the interval power flow, and the accuracy of power flow interval estimation is improved. By utilizing the successive linearization method, the optimal solution can be obtained only by solving a series of linear plans, and the calculation efficiency is high. The purpose of the invention is realized by the following technical scheme:
the linear solving method of the interval reactive power optimization model considers the change of the load and the active output of the generator in a corresponding interval, and comprises the following steps of:
step 1, establishing an interval reactive power optimization model. The active power output and the load of the generator are expressed in an interval form, and then the active power output and the load are substituted into a power flow equation of a deterministic reactive power optimization model, so that an interval reactive power optimization model is obtained.
And 2, dividing variables in the interval reactive power optimization model into two types. One type is a real variable that can be controlled manually, called a control variable, and includes three types: the voltage of the generator terminal (excluding the voltage of a balancing machine), the number of switchable capacitor (or reactance) groups and the transformation ratio of the transformer; the other type is an uncontrollable interval variable which changes along with the control variable, namely a state variable, and comprises a reactive power output of the generator, an active power output of a balanced node, a voltage of a load node and a voltage phase angle of an unbalanced node.
And 3, constructing a linear model of the interval reactive power optimization model. And (3) expanding the interval reactive power optimization model by adopting a Taylor formula (except for an interval power flow equation), expanding a real variable (a control variable) according to a general form, expanding an interval variable (a state variable) at an interval midpoint, and adopting the interval midpoint of the network loss as an objective function. For the state variable, the state variable is expressed in a form of combination of a control variable and a section by using a sensitivity coefficient method, and a section power flow algorithm can be adopted to obtain a corresponding section. In order to ensure the convergence of the algorithm, the iteration step length constraint of the control variable needs to be supplemented in the linearized model.
And 4, solving the linear model of the interval reactive power optimization model by adopting a pure method, and repeatedly iterating. And obtaining a result as an initial value of the next iteration step, and performing loop iteration in such a way until the difference value of the target functions of the previous iteration step and the next iteration step meets the precision requirement.
And 5, outputting a result. The result mainly comprises the change condition of the network loss midpoint value along with the iteration times, the interval distribution condition of possible fluctuation of the state variable after optimization and the optimal control variable.
In the step 1, the step of establishing the interval reactive power optimization model specifically includes:
1) it is assumed that the active power of the generator can be expressed as intervals
Figure GDA0002290853220000041
And
Figure GDA0002290853220000042
wherein SGAnd SLRespectively representing the set of all generators (excluding the balancing machine) and the set of all loads, where SGAnd SLRespectively representing the set of all generators (excluding the balancing machine) and the set of all loads,
Figure GDA0002290853220000043
the lower limit of the active power output fluctuation of the generator,
Figure GDA0002290853220000044
is the upper limit of the active output fluctuation of the generator,
Figure GDA0002290853220000045
the lower limit of the active load fluctuation is,
Figure GDA0002290853220000046
the upper limit of the active load fluctuation is,
Figure GDA0002290853220000047
the lower limit of the reactive load fluctuation is,
Figure GDA0002290853220000048
the upper limit of reactive load fluctuation.
2) The voltage is expressed in polar form:
Figure GDA0002290853220000049
wherein
Figure GDA00022908532200000410
Indicating the node voltage, V, of the i-th nodeiIs the node voltage amplitude of the i-th node, thetaiFor the node voltage phase angle of the ith node and taking the midpoint value of the network loss as an objective function, the interval reactive power optimization model can be expressed as follows:
Figure GDA00022908532200000411
s.t.
Figure GDA0002290853220000051
Figure GDA0002290853220000052
Figure GDA0002290853220000053
in the formula, PlossFor the network loss of the system, S is the set formed by all the nodes of the system, SGAnd SLRespectively representing the set of all generators (excluding the balancing machine) and the set of all loads, STIs a collection of all transformers, SCFor the set of all capacitances (or reactances) involved in compensation, PGiActive generator output, Q, for node iGiIs the reactive power output of the generator at node i,
Figure GDA0002290853220000054
and
Figure GDA0002290853220000055
respectively upper and lower limits, PLiIs the active load of the node, ViIs the node voltage magnitude at node i,
Figure GDA0002290853220000056
and
Figure GDA0002290853220000057
respectively upper and lower limits, GijIs the imaginary part of the ith row and jth column element of the admittance matrix, BijAs the imaginary part, Q, of the ith row and jth column element of the admittance matrixLiFor reactive loading of node i, QCiThe capacitance of the node i is switched for capacity,
Figure GDA0002290853220000058
and
Figure GDA0002290853220000059
respectively, upper and lower limits thereof, TlFor the transformation ratio of the first transformer,
Figure GDA00022908532200000510
and
Figure GDA00022908532200000511
the notation mid {. is used to find the midpoint of an interval.
In the step 2, the variables in the interval reactive power optimization model are divided into control variables and state variables, and the method comprises the following steps:
suppose the node numbering order is: a balance node (No.1), a generator node (nos. 2 to m), a load node (nos. m +1 to n) (where the node with reactive compensation takes precedence (nos. m +1 to m + r)), it may be expressed as u ═ V2…VmQCm+1…QCm+ rT1…Tk]TWherein m is the number of generator nodes (including balancing machine), r is the number of nodes containing capacitance compensation device, n is the number of system nodes, k is the number of transformer, V2…VmFor all generator node voltages (not including balanced node voltage), QCm+1…QCm+rFor all capacitorsCompensating capacity, T1…TkAll transformer transformation ratios are obtained; the state variable is an uncontrollable interval variable comprising reactive power output of the generator, active power output of a balanced node, voltage of a load node and voltage phase angle of an unbalanced node, namely X ═ PG1QG1…QGmVm+1…Vnθ2…θn]TIn which P isG1For balancing the active power of the machine, QG1…QGmFor all generators reactive power, Vm+1…VnFor the voltage amplitude of all load nodes, θ2…θnThe node voltage phase angles are all except the balanced node. Therefore, the interval reactive power optimization model can be simplified into:
Figure GDA0002290853220000061
where f (X, u) is the network loss, h (X, u) is the power flow constraint function, g (X, u) is all inequality constraints (system constraints and operational constraints), [ f (X, u) is the power flow constraint function, andL,fU]and [ h ]L,hU]Respectively corresponding network loss interval and power unbalance interval.
The step of constructing the linearized model of the interval reactive power optimization model in the step 3 is specifically as follows:
1) and expanding the interval reactive power optimization model by adopting a Taylor formula, and neglecting high-order terms of second order and above. For a real variable (control variable) u, the general form is expanded, and for an interval variable (state variable) X, at the midpoint of the interval (X)C,u0) Deployment, XCIs the midpoint of the state variable X, u0Is the initial value of the control variable u. Thus, we can obtain the expansion of each function in equation (5) as follows:
Figure GDA0002290853220000062
Figure GDA0002290853220000063
Figure GDA0002290853220000064
in the formula, f (X)C,u0) Is a point (X)C,u0) Value of grid loss of (h)s(XC,u0) As a function of the current constraint in (X)C,u0) Value of (a), gs(XC,u0) Is an inequality constraint function in the model of (X)C,u0) The value of (a) is (b),
Figure GDA0002290853220000071
and
Figure GDA0002290853220000072
respectively, the objective function to the state variable xiAnd a control variable ujAt point (X)C,u0) The partial derivative of (a) is,
Figure GDA0002290853220000073
and
Figure GDA0002290853220000074
are respectively a power flow constraint function hs(XC,u0) For the state variable xiAnd a control variable ujAt point (X)C,u0) The partial derivative of (a) is,
Figure GDA0002290853220000075
and
Figure GDA0002290853220000076
are respectively inequality constraint functions gs(XC,u0) For the state variable xiAnd a control variable ujAt point (X)C,u0) Partial derivatives of (A), all partial derivatives being constant, NgThe number of inequality constraints is defined, p is the number of state variables, q is the number of control variables, and n is the number of system nodes.
2) For the state variable, it can be expressed as a combination of the control variable and the interval by the following equation (7):
Figure GDA0002290853220000077
in the formula (I), the compound is shown in the specification,
Figure GDA0002290853220000078
to constrain the partial derivatives of the state variables to equality,
Figure GDA0002290853220000079
partial derivatives, X, of the control variables for equality constraintsCIs the midpoint of the state variable X, u0Is the initial value of the control variable u. However, because the high-order expansion terms of interval variables are ignored in the taylor formula of the interval (the width of the interval is not 0), the interval power flow equation cannot be satisfied. In order to enable the final result to meet the interval power flow equation, an interval power flow algorithm is adopted to obtain X-XCThe interval width of (2). Thus, the formula (9) can be rewritten as:
Figure GDA00022908532200000710
wherein r is the interval radius estimated by the interval power flow method, XCIs the midpoint of the state variable X, u0Is the initial value of the control variable u.
3) The state variables in the inequality are replaced. Substituting equation (10) into equation (8) can yield:
gmin≤g(XC,u0)+Ag[-r,r]+B(u-u0)≤gmax， (11)
in the formula (I), the compound is shown in the specification,
Figure GDA00022908532200000711
the partial derivatives of the state variables are constrained for inequality,
Figure GDA00022908532200000712
the partial derivatives of the control variables are constrained for inequality,
Figure GDA0002290853220000081
g(XC,u0) Is constrained at the initial point (X) by inequalityC,u0) The value of (c). Further, by converting the constraint condition of formula (11), it is possible to obtain:
g1 min≤B(u-u0)≤g1 max， (12)
in the formula, g1 max＝min{gmax-g(XC,u0)-Ag[-r,r]Is the new inequality constraint upper limit, g1 min＝max{gmin-g(XC,u0)-Ag[-r,r]And the new inequality constraint lower limit.
4) A linearized model is constructed. First, the objective function only considers the midpoint value of the loss, i.e. the midpoint of the interval of the loss is used as the objective function, i.e. the equation (6) is ignored
Figure GDA0002290853220000082
Term, the objective function is obtained as:
Figure GDA0002290853220000083
in the formula (I), the compound is shown in the specification,
Figure GDA0002290853220000084
is the partial derivative of the objective function with respect to the control variable, f (X)C,u0) Is the value of the objective function at the midpoint. By u(k)Instead of u0And adding step length constraint to the control variable to obtain a linearized iterative model as follows:
Figure GDA0002290853220000085
where k is the number of steps in the current iteration, δ(k)In order to control the step size constraint of the variable,
Figure GDA0002290853220000086
is the objective function value of the k-th generation,fk+1(u) is the objective function value of the k +1 th generation, u(k)Is the value of the control variable of the k-th generation,
Figure GDA0002290853220000087
state variable midpoint values for the k-th generation, δ in order to guarantee convergence of the model (14)(k)Satisfies delta(k)＝δ(k-1)K to maintain a linear descending trend. The optimal solution u obtained by solving is used as u of a next iteration step(k+1)。
In the step 4, a simple method is adopted to solve the linear model of the interval reactive power optimization model, and the steps of repeatedly iterating are as follows:
the objective function value f of the k +1 stepk+1(u) comparing with the k step if
|fk+1-fk|＜ε， (15)
The iteration is stopped. ε in equation (15) is a very small positive number (iteration accuracy), fk+1And fkThe objective function values of the k +1 th generation and the k-th generation are respectively.
The step of outputting the result in the step 5 is specifically as follows:
1) and calculating the distribution interval of the reactive power of the optimized generator by adopting Monte Carlo simulation, outputting the result and drawing.
2) And calculating the distribution interval of the voltage amplitude of the optimized load node by adopting Monte Carlo simulation, outputting the result and drawing.
3) And outputting the network loss midpoint value of the linearization method of the interval reactive power optimization model.
Compared with the prior art, the invention has the following advantages and effects:
(1) the method can be used for solving the reactive power optimization problem of the output and uncertain load of the new energy unit containing wind power, photovoltaic and the like, and provides a safety strategy for the operation of the power grid for dispatching operation workers.
(2) The method adopted by the invention adopts the interval to model the uncertain parameters, needs less information of the uncertain parameters, obtains safe and conservative results and has good convergence, and is beneficial to realizing engineering application.
(3) The method adopts the interval load flow algorithm to obtain the interval of the state variable, and can ensure that the obtained reactive voltage control strategy completely meets the safety constraint of the operation of the power grid.
(4) The method solves the interval reactive power optimization problem by adopting a linearization method, has very quick calculation speed and high efficiency, and can realize online application.
Drawings
Fig. 1 shows the reactive power output distribution intervals of the generator after optimization by an opportunity constraint planning method (abbreviated as CCP) and an interval linearization optimization method (abbreviated as LAM). It can be seen that the reactive power output results of the generator obtained by the optimization of the interval linearization optimization method are all within the set upper and lower reactive power output limits, and the reactive power output of the generator with node 1 obtained by the optimization of the opportunity constraint planning method is out of limit.
Fig. 2 shows load voltage amplitude intervals after optimization by an opportunistic constraint programming method (abbreviated as CCP) and an interval linearization optimization method (abbreviated as LAM). It can be seen that the load node voltage results obtained by both methods are within the set upper and lower limits of the load node voltage.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
Examples
For the purpose of facilitating an understanding of the present invention, reference is made to the following description taken in conjunction with the accompanying drawings.
The modified IEEE30 node system is adopted for testing, and the system comprises 37 transmission lines, 4 transformers, 1 reactive compensation point, 6 generating sets (No.1 is a balance set) and 24 load nodes. Assuming that active power output and load of all the generators have a fluctuation interval of +/-30%, the parameters are calculated by adopting a per-unit system, and the reference power is 100M V & A. In order to facilitate drawing, nodes of the system are numbered again, wherein the number 1 is a balance node, the numbers 2-6 are common generator nodes, the numbers 7-30 are load nodes, and the original sequence of the nodes of the same type is unchanged.
The following specifically describes the algorithm steps of the rectangular coordinate interval load flow calculation:
in the first step, the data of the system node (here, IEEE30 node data) is read. Including network parameters, unit and load parameters, setting iteration precision epsilon as 10-4And an initial step size limit delta(0)＝1。
And step two, solving a linear model of the interval reactive power optimization model by adopting a pure method, and repeatedly iterating. And performing loop iteration in such a way until the difference value of the target functions of the previous iteration step and the next iteration step meets the precision requirement. Meanwhile, in the process, an interval of the state variables needs to be obtained by using an interval flow method based on affine arithmetic so as to eliminate the interval variables in the optimization model.
And thirdly, outputting a result. The method comprises a voltage and generator reactive power output interval (obtained by adopting a Monte Carlo model) and the condition that a point value in a network loss interval changes along with the iteration number.
To further verify the effectiveness and superiority of the linearized solution method of the interval reactive power optimization model, we compared the method proposed herein with opportunity Constrained Programming (CCP). For opportunity constrained planning, the model can be expressed as:
Figure GDA0002290853220000101
Figure GDA0002290853220000102
wherein f (x, u) is the network loss, h (x, u) is ξ is the interval power flow equation, ξ is the active output and load of the generator, which are random variables in the fluctuation interval, and the active output and load of the generator are assumed to be uniformly distributed in the respective fluctuation interval, and gmin≤g(x,u)≤gmaxBoth the confidence levels α and β are constraints for state variables and control variables, where for comparison to the interval algorithm, the confidence level α is 1 and β is 0.5 for the opportunistic constraint planning model (16), the dead weight is utilizedAnd (4) solving by using an algorithm. The method is realized by adopting MATLAB software programming, the distribution interval of the reactive power of the generator is shown in figure 1 (CCP represents an opportunity constraint programming method, LAM represents a linear solving method of an interval reactive power optimization model), and the interval distribution condition of the voltage of the load node is shown in figure 2. As can be seen from fig. 1, the control strategy obtained by adopting the opportunity constraint programming may cause the reactive power output of the generator to exceed the limit (for example, node 1 in the figure), thereby verifying that the reactive voltage control strategy obtained by the linearization method of the interval reactive power optimization model has higher security. As can be seen from fig. 2, both the CCP method and the LAM method can ensure that the voltage amplitude of the load node is within the set upper and lower voltage limits. The calculation time and the objective function result of the two algorithms are shown in table 1, and it can be seen that the time required by the linearization method is much shorter than that of the CCP method. The above analysis shows that the linearization algorithm of the interval reactive power optimization model can not only obtain the reactive voltage control strategy which completely meets the constraint condition, but also has less calculation time and higher calculation efficiency compared with the traditional opportunity constraint planning.
Figure GDA0002290853220000111
TABLE 1
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims (5)

1. The linear solving method of the interval reactive power optimization model is characterized by comprising the following steps of:
step 1, establishing an interval reactive power optimization model; the active power output and the load of the generator are both expressed in an interval form, and then the active power output and the load are substituted into a power flow equation of a deterministic reactive power optimization model to obtain an interval reactive power optimization model;
step 2, dividing variables in the interval reactive power optimization model into two types; one type is a real variable that can be controlled manually, called a control variable, which includes three types: the voltage of the generator terminal, the number of switchable capacitors or reactance groups and the transformation ratio of the transformer are different from the voltage of the balancing machine; the other type of the variable is an uncontrollable interval variable which changes along with a control variable and is called a state variable, wherein the state variable comprises reactive power output of a generator, active power output of a balanced node, voltage of a load node and a voltage phase angle of an unbalanced node;
step 3, constructing a linear model of the interval reactive power optimization model; expanding an interval reactive power optimization model except for an interval power flow equation by using a Taylor formula, expanding a real variable, namely a control variable, according to a general form, expanding an interval variable, namely a state variable, at the midpoint of the interval, and taking the midpoint of the interval with the network loss as a target function; for the state variable, expressing the state variable into a form of combination of a control variable and an interval by using a sensitivity coefficient method, and acquiring a corresponding interval by using an interval power flow algorithm; in order to ensure the convergence of the algorithm, the iteration step length constraint of the control variable is supplemented in the linear model;
step 4, solving a linear model of the interval reactive power optimization model by adopting a pure method, and repeatedly iterating; obtaining a result as an initial value of the next iteration step, and performing loop iteration until the difference value of the target functions of the previous iteration step and the next iteration step meets the precision requirement;
step 5, outputting a result; the result comprises the change condition of the grid loss midpoint value along with the iteration times, the interval distribution condition of the state variable possibly fluctuating after optimization and the optimal control variable;
in step 3, the step of constructing the linearized model of the interval reactive power optimization model is specifically as follows:
step 31, expanding the interval reactive power optimization model by using a Taylor formula, and neglecting high-order terms of second order and above; the control variable u, which is a real variable, is developed in a general form, and the state variable X, which is an interval variable, is developed at an interval midpoint (X)C,u0) Deployment, XCIs the midpoint of the state variable X, u0For the initial values of the control variable u, the expansion of each function in equation (5) is obtained as follows:
Figure FDA0002290853210000021
Figure FDA0002290853210000022
Figure FDA0002290853210000023
in the formula, f (X)C,u0) Is a point (X)C,u0) Value of grid loss of (h)s(XC,u0) As a function of the current constraint in (X)C,u0) Value of (a), gs(XC,u0) Is an inequality constraint function in the model of (X)C,u0) The value of (a) is (b),
Figure FDA0002290853210000024
and
Figure FDA0002290853210000025
respectively, the objective function to the state variable xiAnd a control variable ujAt point (X)C,u0) The partial derivative of (a) is,
Figure FDA0002290853210000026
and
Figure FDA0002290853210000027
are respectively a power flow constraint function hs(XC,u0) For the state variable xiAnd a control variable ujAt point (X)C,u0) The partial derivative of (a) is,
Figure FDA0002290853210000028
and
Figure FDA0002290853210000029
are respectively inequality constraint functions gs(XC,u0) For the state variable xiAnd a control variable ujAt point (X)C,u0) Partial derivatives of (A), all partial derivatives being constant, NgThe number of inequality constraints is defined, p is the number of state variables, q is the number of control variables, and n is the number of system nodes;
and step 32, regarding the state variable, representing the state variable into a form of combination of a control variable and an interval by using an equation (7), wherein the equation is as follows:
Figure FDA0002290853210000031
in the formula (I), the compound is shown in the specification,
Figure FDA0002290853210000032
to constrain the partial derivatives of the state variables to equality,
Figure FDA0002290853210000033
partial derivatives, X, of the control variables for equality constraintsCIs the midpoint of the state variable X, u0Is the initial value of the control variable u; however, because a high-order expansion term of an interval variable is neglected in the Taylor formula of the interval, the width of the interval is not 0, and the interval power flow equation cannot be satisfied; in order to enable the final result to meet the interval power flow equation, an interval power flow algorithm is adopted to obtain X-XCThe interval width of (2) is rewritten as:
Figure FDA0002290853210000034
wherein r is the interval radius estimated by the interval power flow method, XCIs the midpoint of the state variable X, u0Is the initial value of the control variable u;
and step 33, replacing the state variables in the inequality, and substituting the equation (10) into the equation (8) to obtain:
gmin≤g(XC,u0)+Ag[-r,r]+B(u-u0)≤gmax， (11)
in the formula (I), the compound is shown in the specification,
Figure FDA0002290853210000035
the partial derivatives of the state variables are constrained for inequality,
Figure FDA0002290853210000036
the partial derivatives of the control variables are constrained for inequality,
Figure FDA0002290853210000037
g(XC,u0) Is constrained at the initial point (X) by inequalityC,u0) The constraint of equation (11) is transformed to yield:
g1 min≤B(u-u0)≤g1 max， (12)
in the formula, g1 max＝min{gmax-g(XC,u0)-Ag[-r,r]Is the new inequality constraint upper limit, g1 min＝max{gmin-g(XC,u0)-Ag[-r,r]The new inequality constraint lower limit;
step 34, constructing a linearization model; firstly, the objective function only considers the midpoint value of the network loss, i.e. the midpoint of the interval of the network loss is taken as the objective function, and the equation (6) is ignored
Figure FDA0002290853210000038
Term, the objective function is obtained as:
Figure FDA0002290853210000039
in the formula (I), the compound is shown in the specification,
Figure FDA0002290853210000041
is the partial derivative of the objective function with respect to the control variable, f (X)C,u0) As an objective function inThe value at the midpoint; by u(k)Instead of u0And adding step length constraint to the control variable to obtain a linearized iterative model as follows:
Figure FDA0002290853210000042
where k is the number of steps in the current iteration, δ(k)In order to control the step size constraint of the variable,
Figure FDA0002290853210000043
is the objective function value of the k generation, fk+1(u) is the objective function value of the k +1 th generation, u(k)Is the value of the control variable of the k-th generation,
Figure FDA0002290853210000044
state variable midpoint values for the k-th generation, δ in order to guarantee convergence of the model (14)(k)Satisfies delta(k)＝δ(k-1)K, to maintain a linear descending trend; the optimal solution u obtained by solving is used as u of a next iteration step(k+1)。
2. The method for solving the interval reactive power optimization model in a linearized manner according to claim 1, wherein in the step 1, the step of establishing the interval reactive power optimization model specifically includes:
step 11, assuming that the active power output of the generator can be expressed as intervals
Figure FDA0002290853210000045
for i∈SG，
Figure FDA0002290853210000047
And
Figure FDA0002290853210000048
for i∈SLwherein S isGAnd SLRepresenting the aggregate of all generators except the balancing machine and all loadsIn the collection of the images, the image data is collected,
Figure FDA0002290853210000049
the lower limit of the active power output fluctuation of the generator,
Figure FDA00022908532100000410
is the upper limit of the active output fluctuation of the generator,
Figure FDA00022908532100000411
the lower limit of the active load fluctuation is,
Figure FDA00022908532100000412
the upper limit of the active load fluctuation is,
Figure FDA00022908532100000413
the lower limit of the reactive load fluctuation is,
Figure FDA00022908532100000414
is the upper limit of reactive load fluctuation;
and step 12, expressing the voltage in a polar coordinate form:
Figure FDA00022908532100000415
wherein the content of the first and second substances,
Figure FDA00022908532100000416
indicating the node voltage, V, of the i-th nodeiIs the node voltage amplitude of the i-th node, thetaiFor the node voltage phase angle of the ith node and taking the midpoint value of the network loss as an objective function, the interval reactive power optimization model can be expressed as follows:
Figure FDA00022908532100000417
s.t.
Figure FDA00022908532100000418
Figure FDA0002290853210000051
Figure FDA0002290853210000052
in the formula, PlossFor the network loss of the system, S is the set formed by all the nodes of the system, SGAnd SLRespectively representing the set of all generators except the balancing machine and the set of all loads, STIs a collection of all transformers, SCFor the set of all capacitances or reactances participating in the compensation, PGiActive generator output, Q, for node iGiIs the reactive power output of the generator at node i,
Figure FDA0002290853210000053
and
Figure FDA0002290853210000054
respectively upper and lower limits, PLiIs the active load of the node, ViAmplitude of node voltage, V, for node ii maxAnd Vi minRespectively upper and lower limits, GijIs the imaginary part of the ith row and jth column element of the admittance matrix, BijAs the imaginary part, Q, of the ith row and jth column element of the admittance matrixLiFor reactive loading of node i, QCiThe capacitance of the node i is switched for capacity,
Figure FDA0002290853210000055
and
Figure FDA0002290853210000056
respectively, upper and lower limits thereof, TlFor the first transformer transformation ratio, Tl maxAnd Tl minThe symbol mid {. is denoted as "mid {. cndot.") representing an intervalThe midpoint of (a).
3. The method for solving the linearity of the reactive power optimization model according to claim 1, wherein in the step 2, the specific method for dividing the variables in the reactive power optimization model into the control variables and the state variables is as follows:
suppose the node numbering order is: balance node No.1, generator nodes No. 2-m, load nodes No. m + 1-n, wherein the node with reactive compensation has priority No. m + 1-m + r, which is expressed as u ═ V ═ m2…VmQCm+1…QCm+rT1…Tk]TWherein m is the number of generator nodes including the balancing machine, r is the number of nodes including the capacitance compensation device, n is the number of system nodes, k is the number of transformers, and V2…VmFor all generator node voltages except the balanced node voltage, QCm+1…QCm+rFor compensating the capacity, T, for all capacitances1…TkAll transformer transformation ratios are obtained; the state variable is an uncontrollable interval variable and comprises reactive power output of the generator, active power output of a balanced node, voltage of a load node and a voltage phase angle of an unbalanced node, namely X ═ PG1QG1…QGmVm+1…Vnθ2…θn]TWherein P isG1For balancing the active power of the machine, QG1…QGmFor all generators reactive power, Vm+1…VnFor the voltage amplitude of all load nodes, θ2…θnThe node voltage phase angles of all the nodes except the balance node; the interval reactive power optimization model is simplified into:
Figure FDA0002290853210000061
wherein f (X, u) is network loss, h (X, u) is a power flow constraint function, g (X, u) is all inequality constraints, the inequality constraints comprise system constraints and operation constraints, and [ fL,fU]And [ h ]L,hU]Respectively corresponding network loss interval and powerAnd unbalance interval.
4. The method for solving the interval reactive power optimization model in a linearized manner according to claim 1, wherein in step 4, the linearized model of the interval reactive power optimization model is solved by a simplex method, and the method for repeating iteration specifically comprises the following steps:
the objective function value f of the k +1 stepk+1(u) comparing with the k step if:
|fk+1-fk|＜ε， (15)
stopping iteration; in the formula (15), epsilon is a very small positive number, epsilon is iteration precision, and fk+1And fkThe objective function values of the k +1 th generation and the k-th generation are respectively.
5. The linear solving method of the interval reactive power optimization model according to claim 1, wherein the step of outputting the result in the step 5 is specifically as follows:
51, calculating a distribution interval of the optimized reactive power of the generator by adopting Monte Carlo simulation, outputting a result and drawing;
step 52, calculating the distribution interval of the voltage amplitude of the optimized load node by adopting Monte Carlo simulation, outputting the result and drawing;
and step 53, outputting the network loss midpoint value of the linearization method of the interval reactive power optimization model.
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